Notes on the spectral properties of the weighted mean difference operator G (u, v; δ) over the sequence space ℓ1


KARAKAYA V. , ERDOĞAN E.

Acta Mathematica Scientia, vol.36, no.2, pp.477-486, 2016 (Journal Indexed in SCI Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 2
  • Publication Date: 2016
  • Doi Number: 10.1016/s0252-9602(16)30014-5
  • Title of Journal : Acta Mathematica Scientia
  • Page Numbers: pp.477-486

Abstract

© 2016 Wuhan Institute of Physics and Mathematics.In the study by Baliarsingh and Dutta [Internat. J.Anal., Vol.2014(2014), Article ID 786437], the authors computed the spectrum and the fine spectrum of the product operator G (u, v; δ) over the sequence space ℓ1. The product operator G (u, v; δ) over ℓ1 is defined by (G(u,v; δ)x)k=∑i=0kukvi(xi-xi-1) with xk = 0 for all k < 0, where x = (xk) ∈ ℓ1, and u and v are either constant or strictly decreasing sequences of positive real numbers satisfying certain conditions. In this article we give some improvements of the computation of the spectrum of the operator G (u, v; δ) on the sequence space ℓ1.